Errrr......... 1ppm error is approx 2.6 times greater than one second per month.
If you want to calibrate to that level of accuracy you'd need a reference oscillator with an order of magnitude better accuracy and stability. The BK precision frequency counter you linked is
only 1ppm, so as-is you wouldn't have a hope of trimming close than 5 seconds per month. However it does support using an external timebase, so if you also get a 10MHz GPSDO to drive its rear panel external timebase input you could achieve the required accuracy.
However I strongly doubt that the RTCCs you are using have sufficient long term stability to be calibrated as you hope.
If you don't need to be able to measure frequencies above 100MHz, a seven digit frequency counter built around a PIC18 MCU is reasonably simple, cheap to build and fairly easy to code. With a little more thought, its resolution can be extended in software to an arbitrary number of digits, at the cost of requiring an order of magnitude increase in gate time for each digit. Accuracy will be as good as its clock source.